Name ________________________________________ Date __________________ Class __________________
LESSON
25-2
Slope and Perpendicular Lines
Practice and Problem Solving: A/B
Line A contains the points (−1, 5) and (1, −3). Line B contains the
points (2, 3) and (−2, 2).
1. Are the lines perpendicular? Explain your reasoning.
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Figure WXYZ has as its vertices the points W(2, 7), X(5, 6), Y(5, −4),
and Z(−1, −2).
Find each slope.
2. WX
3. XY
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4. YZ
_______________
_______________
5. ZW
________________
6. Is Figure WXYZ a rectangle? Explain your reasoning.
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For Problems 7–10, use the graph at the right.
7. Find the slope of line A.
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8. Explain how you found the slope.
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9. Line t is perpendicular to line A and passes through point K.
Find the slope of line t.
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10. Find the equation of line t. Explain how you found the equation.
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Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
475
2. y =
1
3
1
3
x + − or y = x −
2
2
2
2
2
x − 3; Possible answer: The slope,
3
2
m, is . The y-intercept, b, is −3. The
3
2
equation, y = mx + b, is y = x − 3.
3
10. y =
3. Possible answers: The equation will be
the same because it is the same line; or,
the equations will be different because the
points used are different. (Note: This
question asks the student to make a
hypothesis before completing a
procedure. It is acceptable if the initial
hypothesis is incorrect.)
Practice and Problem Solving: C
1. y = −6x + 16
2. y =
4. No. The two
HJJG lines are not parallel, so the
slope of HJJ
ABG cannot be used to find the
slope of CD.
1
x+2
3
3. x = 2
4. y = 7
Success for English Learners
1. Possible answer: y = 2 x − 1 and
y = 2x + 5
5. The slopes of the lines are
3
. The quadrilateral is a
2
parallelogram.
and −
2. No. On a trapezoid, there is only one set
of parallel sides.
LESSON 25-2
6. k = −10
Practice and Problem Solving: A/B
7. h = 17
8. n = −7
1. Yes; Possible answer: The slopes of the
1
lines are −4 and . The product of the
4
slopes of the lines is −1. Two non-vertical
lines are perpendicular if and only if the
product of their slopes is −1.
1
2. −
3
9. m = −
1. −
1
2
2. 2
3. Yes; the product of their slopes is −1, so
the segments are perpendicular.
1
3
4. −2
5. 3
5. −2
6. No; Possible answer: WX and YZ are
parallel and both are perpendicular to
ZW . However, XY is not parallel to ZW .
So, the figure is a trapezoid.
3
7. −
2
6. No; Possible answer: The slope of each
line is −2, so the product of their slopes is
4, not −1. Since the slopes are equal, the
lines are parallel.
7. A rectangle has four right angles. So,
show that adjacent line segments are
perpendicular.
8. Possible answer: (0, 3) and (2, 0) are two
points on the line.
3−0 3
3
slope =
=
=−
0 − 2 −2
2
9.
1
or m = 0
2
Practice and Problem Solving:
Modified
3. undefined slope (The segment is vertical.)
4. −
2
3 2
, − , ,
3
2 3
8. −
9.
2
3
2
3
3
2
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
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